Overview
Today you may be the adjoining owner. In five years you may want a loft conversion, rear extension, basement, structural alteration or other work that requires you to serve your own Party Wall notice. At that point the roles reverse.
There is no statutory rule saying that, because you caused your neighbour to spend more on this project, they are entitled to make you spend more on yours. This is a practical point about human behaviour and neighbour relations, not a legal penalty.
Reciprocity is real even when it is not written into the Act
If you insisted on two surveyors where one would plainly have worked, encouraged unnecessary referrals, rejected sensible arrangements or treated every minor issue as a battle, your neighbour may remember that when your own notice arrives.
They may then choose their own surveyor rather than an agreed surveyor, scrutinise every request more closely, be less willing to accommodate early starts or access arrangements, and generally insist upon the full formal process. They are entitled to make their own decisions, just as you are.
That does not mean you should waive genuine protection
You should never consent to something unsafe or give up a protection you genuinely need simply to remain friendly. The point is proportionality. There is a difference between protecting your property and deliberately maximising the other owner’s cost.